Abstract: In the study of electron transport within lattice materials, the temporal and spatial scales generally cover a wide range. These multiscale nature leads to significant challenges for numerical simulations. In this work, we present a discrete unified gas-kinetic scheme infinite volume framework for solving the electron Boltzmann transport equation under the condition of weak temperature fields. Our method innovatively employs characteristic solution at cell interfaces in the flux reconstruction, achieving a second-order spatial accuracy with low numerical dissipation. A notable feature of this scheme is its decoupling of the time step from the relaxation time; instead, the time step is only determined by the Courant-Friedrichs-Lewy (CFL) condition. This characteristic ensures an enhanced asymptotic preservation across a spectrum from ballistic to diffusive regimes. The efficiency and accuracy of the proposed method are validated by a series of test cases involving a wide range of Knudsen numbers. The results confirm the robustness and accuracy of the method, demonstrating its potential as an effective numerical tool for the study of electron heat transfer in metals.